The Gmail app doesn't take up as much space as you think. On my phone, its using maybe 10 MB total, cache and all. On most modern Android phones, that's virtually nothing. And I have several thousand emails in my Inbox because I keep forgetting to delete them with 1 GB of my 10 GB used.
It isn't actually storing emails on the phone like POP and IMAP email systems do, they are just temporarily cached for a short time so you don't have to keep redownloading your latest email every time you open the app. They are constantly being downloaded and purged from the phone as you receive new email and after that, only loaded "on-demand" when you scroll past the first few messages.
So in other words, just let the Gmail app do its thing. Don't worry about how much space its using, since its definitely nowhere near many apps like the web browser.